Design Optimization Of Composite Laminated Plates And Optimal Layout Of Attached MFC Patches For Vibration Suppression

The vibration of structures can be well suppressed by carrying out dynamic structura l optimization.Normally,the vibration responses of structures made by traditional materials can be reduced by optimizing the distribution of materials.Piezoelectric materials can be introduced in traditional structures to achieve vibration control due to the capacity of mechanical energy and electrical energy conversion of piezoelectric materials.A large number of scholars focus on minimizing the vibration responses of structures.Therefore,several performance indexes have been proposed to describe vibration responses,e.g.the local structural response and the average input power of the mechanical loading,etc.Besides,the simplification of piezoelectr ic effects has been studied,e.g.considering piezoelectric effects as induced force and active damping,etc.Based on recent design optimization methods for piezoelectric material structures and composite structures,the main purpose of this paper is to develop an effective optimiza t io n approach for vibrating piezoelectric composite structures.The approach will consider design optimization of material selection,fiber orientation and stack sequences of composite structures;simultaneously,with the layout optimization of bonded MFC patches with prescribed sizes.Besides,the manufacturability of optimized designs will be taken into consideration during optimization.The contexts of this paper are following as:(1)The classical topological optimization methods and design optimization for composite structures are summarized.The material model for piezoelectric material,the simplified piezoelectric effects model,the finite element model and the vibration analysis model of piezoelectric material structures are established.Meanwhile,the applications of piezoelectr ic materials for vibration suppression are discussed.(2)Based on the Discrete Material Optimization(DMO)method,Piezoelectric Material with Penalization(PEMAP)model and dynamic optimization model,this paper develops an effective optimization approach for minimizing the vibration response of piezoelectr ic laminated plates.The average input power of mechanical loading over a cycle of excitatio n frequency and the global structural response are used as objective function,respectively.The optimization problems are solved by using the gradient based method — the method of moving asymptotes(MMA),and the sensitivities are derived from the adjoint-variable method.(3)The optimization approach is employed in the design optimization of a piezoelectr ic laminated plate for suppressing vibration.The optimized designs obtained from differe nt excitation frequencies and loading conditions are compared and discussed.These numeric a l examples are used to demonstrate the effectiveness of the proposed method.(4)The patch design variables are introduced in the piezoelectric layer to simulate the effect of prescribed sizes MFC patches.The optimized designs obtained from the new optimization model are compared with the optimized designs without considering the sizes of MFC to illuminate the effectiveness of this new approach.Besides,the continuity of the fiber are improved by carrying out numerical post-processing for optimized results.